High Energy Astrophysics 5 JAN, 2015

Current Flow and Pair Creation at Low Altitude in Rotation Powered Pulsars Force-Free Magnetospheres: Space-Charge Limited Flow

Current Flow and Pair Creation at Low Altitude in Rotation Powered Pulsars Force-Free Magnetospheres: Space-Charge Limited Flow

(shortened) We report the results of an investigation of particle acceleration and electron-positron plasma generation at low altitude in the polar magnetic flux tubes of Rotation Powered Pulsars, when the stellar surface is free to emit whatever charges and currents are demanded by the force-free magnetosphere. We observe novel behavior. a) When the current density is less than the Goldreich-Julian (GJ) value (0<j/j_{GJ}<1), space charge limited acceleration of the current carrying beam is mild, with the full GJ charge density being comprised of the charge density of the beam, co-existing with a cloud of electrically trapped particles with the same sign of charge as the beam. The voltage drops are on the order of mc^2/e, and pair creation is absent. b) When the current density exceeds the GJ value (j/j_{GJ}>1), the system develops high voltage drops, causing emission of gamma rays and intense bursts of pair creation. The bursts exhibit limit cycle behavior, with characteristic time scales somewhat longer than the relativistic fly-by time over distances comparable to the polar cap diameter (microseconds). c) In return current regions, where j/j_{GJ}<0, the system develops similar bursts of pair creation. In cases b) and c), the intermittently generated pairs allow the system to simultaneously carry the magnetospherically prescribed currents and adjust the charge density and average electric field to force-free conditions. We also elucidate the conditions for pair creating beam flow to be steady, finding that such steady flows can occupy only a small fraction of the current density parameter space of the force-free magnetospheric model. The generic polar flow dynamics and pair creation is strongly time dependent. The model has an essential difference from almost all previous quantitative studies, in that we sought the accelerating voltage as a function of the applied current.

💡 Research Summary

The paper investigates particle acceleration and electron‑positron pair creation in the low‑altitude polar flux tubes of rotation‑powered pulsars under the assumption that the stellar surface can emit any charge and current demanded by a force‑free magnetosphere. By solving the space‑charge‑limited flow (SCLF) problem with the current density j prescribed, the authors obtain the accelerating voltage as a function of j and explore three distinct regimes defined by the ratio α = j/j_GJ, where j_GJ is the Goldreich‑Julian current density.

  1. Sub‑Goldreich‑Julian regime (0 < α < 1). The current‑carrying electron beam experiences only mild acceleration, with voltage drops of order ΔV ≈ mc²/e. The beam’s charge density together with a co‑existing cloud of trapped particles of the same sign exactly reproduces the GJ charge density, so the net charge density matches the force‑free requirement. The electric field is too weak to produce high‑energy photons, and consequently no pair creation occurs.

  2. Super‑Goldreich‑Julian regime (α > 1). When the imposed current exceeds the GJ value, the electric field grows to produce voltage drops far larger than mc²/e. Electrons are accelerated to ultra‑relativistic energies, emit curvature or inverse‑Compton γ‑rays, and trigger prolific pair creation via γ‑B or γ‑γ processes. The pair production is not steady; instead it occurs in quasi‑periodic bursts that form a limit‑cycle with a characteristic timescale of a few microseconds—comparable to the light‑crossing time of the polar‑cap diameter. The intermittently created pairs adjust the local charge density and average electric field so that the global force‑free current is sustained.

  3. Return‑current regime (α < 0). In regions where the current flows opposite to the GJ direction, the system exhibits the same bursty pair‑creation behavior as in the super‑GJ case. The generated pairs again serve to balance the charge density and keep the prescribed current flowing.

A key finding is that truly steady, pair‑producing beam solutions occupy only a narrow slice of the α‑parameter space (essentially α≈1±ε). In the vast majority of the force‑free magnetospheric model’s current distribution, the polar flow is intrinsically time‑dependent and characterized by intermittent high‑voltage episodes and pair‑creation bursts. By explicitly calculating the voltage as a function of the applied current, the study departs from earlier works that either imposed a voltage or derived the current a posteriori. The results have important implications for pulsar high‑energy emission, radio‑pulse microstructure, and the global electrodynamics of pulsar magnetospheres, suggesting that observed variability may be a direct manifestation of the limit‑cycle dynamics described here.